I. Introduction


Table 1.Sample for 5 randomly chosen countries of the data set used in this study
Country agricultural_land_p_2016 forest_area_p_2015 population_growth_p_2015
Georgia 34.45100 40.61591 0.1574814
Pacific island small states 13.43769 61.56636 1.3132995
Nauru 20.00000 0.00000 5.1145642
Indonesia 31.46442 50.23819 1.2674656
Cyprus 12.15693 18.69048 0.7521855
Country aded_val_GDP_2015 perm_cropLand_p_2015
Georgia 7.813762 1.582962
Pacific island small states 11.906936 5.961059
Nauru 4.196069 20.000000
Indonesia 13.492644 12.420166
Cyprus 1.874272 2.857143

II. Exploratory data analysis


Table 2: Summary for the percent of agricultural land in different countries, in 2016
n min median mean max sd
225 0.5576923 39.275 38.90696 82.55971 19.67133
Figure 1. Distribution for the percent of agricultural land in different countries, in 2016

Figure 1. Distribution for the percent of agricultural land in different countries, in 2016

Figure 4. Interactive Scatterplot for the percent of agricultural land in different countries, in 2016 against their 2015 Permanent Crop Land (% of land area). The red line is the best fit line. The blue curve is the Loess curve.

Figure 5. Interactive Scatterplot for the percent of agricultural land in different countries, in 2016 against their percent of forest area, in 2015. The red line is the best fit line. The blue curve is the Loess curve.

Figure 8. Interactive Scatterplot for the percent of agricultural land in different countries, in 2016 against their percent annual population growth in 2015. The red line is the best fit line. The blue curve is the Loess curve.

Figure 9. Interactive Scatterplot for the percent of agricultural land in different countries, in 2016 against the % added value of Agriculture, forestry, and fishing to their GDP in 2015. The red line is the best fit line. The blue curve is the Loess curve.


III. Multiple linear regression

i. Methods


The model is:

## lm(formula = agricultural_land_p_2016 ~ perm_cropLand_p_2015 + 
##     ns(population_growth_p_2015, df = 4) + ns(forest_area_p_2015, 
##     df = 4) + ns(aded_val_GDP_2015, df = 4), data = tidy_joined_dataset)
Figure 10. Normal Q-Qplot for the percent of agricultural land in different countries, in 2016

Figure 10. Normal Q-Qplot for the percent of agricultural land in different countries, in 2016

Table 3: VIF table
GVIF Df GVIF^(1/(2*Df))
perm_cropLand_p_2015 1.124085 1 1.060229
ns(population_growth_p_2015, df = 4) 2.421891 4 1.116913
ns(forest_area_p_2015, df = 4) 1.490688 4 1.051171
ns(aded_val_GDP_2015, df = 4) 2.007460 4 1.091015

ii. Model Results and Interpretation


## lm(formula = agricultural_land_p_2016 ~ perm_cropLand_p_2015 + 
##     ns(population_growth_p_2015, df = 4) + ns(forest_area_p_2015, 
##     df = 4) + ns(aded_val_GDP_2015, df = 4), data = tidy_joined_dataset)
Table 4. Model Summary Table
Estimate Std. Error t value Pr(>|t|)
(Intercept) 24.1215 10.3841 2.3229 0.0211
perm_cropLand_p_2015 0.4914 0.1434 3.4269 0.0007
ns(population_growth_p_2015, df = 4)1 -9.6982 8.5759 -1.1309 0.2594
ns(population_growth_p_2015, df = 4)2 10.3611 7.9389 1.3051 0.1933
ns(population_growth_p_2015, df = 4)3 -20.9933 19.8490 -1.0576 0.2914
ns(population_growth_p_2015, df = 4)4 -42.8759 11.5787 -3.7030 0.0003
ns(forest_area_p_2015, df = 4)1 -0.5732 4.3938 -0.1305 0.8963
ns(forest_area_p_2015, df = 4)2 -19.1007 5.0858 -3.7557 0.0002
ns(forest_area_p_2015, df = 4)3 2.6878 9.8495 0.2729 0.7852
ns(forest_area_p_2015, df = 4)4 -49.7971 7.6792 -6.4847 0.0000
ns(aded_val_GDP_2015, df = 4)1 15.5354 4.4557 3.4866 0.0006
ns(aded_val_GDP_2015, df = 4)2 7.3391 6.7614 1.0854 0.2790
ns(aded_val_GDP_2015, df = 4)3 42.0494 10.6767 3.9384 0.0001
ns(aded_val_GDP_2015, df = 4)4 13.8894 11.0561 1.2563 0.2104
Value df
Residual Standard Error 14.926 211
Multiple R-squared 0.458
Adjusted R-squared 0.424
Value Numerator df Denominator df
Model F-statistic 13.7 13 211
P-value 7.366e-22

iii. Inference for multiple regression

Table 5. ANOVA (Type II tests) Table
Sum Sq Df F value Pr(>F)
perm_cropLand_p_2015 2616.434 1 11.7435 0.0007
ns(population_growth_p_2015, df = 4) 3295.916 4 3.6983 0.0062
ns(forest_area_p_2015, df = 4) 27741.579 4 31.1287 0.0000
ns(aded_val_GDP_2015, df = 4) 4420.418 4 4.9601 0.0008
Residuals 47010.294 211 NA NA

Figure 13. Interactive Scatterplot for the percent of agricultural land in different countries, in 2016 against their 2015 Permanent Crop Land (% of land area), where the forest area percentage of a country’s land in 2015 euqals its median = 31.88387, for a median percent population growth in a country in 2015 = 1.256186, and for a median % added value of agriculture, forestry, and fishing to the GDP of a country = 7.408892. The blue line is the linear curve, with its associated 95% CI and wider pink 95% PI.

Figure 14. Interactive Scatterplot for the percent of agricultural land in different countries, in 2016 against their percent annual population growth in 2015, where the forest area percentage of a country’s land in 2015 euqals its median = 31.88387, for a median % added value of agriculture, forestry, and fishing to the GDP of a country = 7.408892, and for a median percent of permanent crop land of a country’s land area = 1.311853. The blue line is the natural spline, with its associated 95% CI and wider pink 95% PI.

Figure 15. Interactive Scatterplot for the percent of agricultural land in different countries, in 2016 against their percent of forest area, in 2015, for a median percent population growth in a country in 2015 = 1.256186, for a median % added value of agriculture, forestry, and fishing to the GDP of a country = 7.408892, and for a median percent of permanent crop land of a country’s land area = 1.311853. The blue line is the natural spline, with its associated 95% CI and wider pink 95% PI.

Figure 16. Interactive Scatterplot for the percent of agricultural land in different countries, in 2016 against the % added value of Agriculture, forestry, and fishing to their GDP in 2015, where the forest area percentage of a country’s land in 2015 euqals its median = 31.88387, for a median percent population growth in a country in 2015 = 1.256186, and for a median percent of permanent crop land of a country’s land area = 1.311853. The blue line is the natural spline, with its associated 95% CI and wider pink 95% PI.

IV. Discussion

i. Conclusions

ii. Limitations

iii. Further questions


V. Citations and References